Question

Two different dice are thrown together.Write all the possible outcomes.
Find the probability that the product of the numbers appearing on the top
of the dice is less than 9.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

A  die has 6 faces marked as 1,2, 3, 4, 5, 6. When we throw a die , than total number of  outcomes = 6   {  1 , 2 , 3 , 4 , 5 , 6 }

But when we throw  two dice simultaneously , than total number of outcomes =  6 × 6 = 36

Total possible outcomes on throwing two dice are:

{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6), (2,1),(2,2),(2,3),(2,4),(2,5),(2,6), (3,1),(3,2),(3,3),(3,4),(3,5),(3,6), (4,1),(4,2),(4,3),(4,4),(4,5),(4,6), (5,1),(5,2),(5,3),(5,4),(5,5),(5,6), (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}


Number of all possible outcomes=36


Let E = product  of the numbers appearing on the top of the dice is less than 9


Favourable outcomes are(E) : (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(4,1) ,(4,2),(5,1),(6,1)


Number of outcomes favourable to(E)=16


P(E)= number of favourable outcomes/total number of outcomes


P(E)= 16/36


P(E)= 4/9


Hence, P(E)= 4/9


Hope this will help you....